Late Friday afternoon, President Obama said that the two parties are not that far apart from compromise. The President advised elected officials to go home, have some eggnog and Christmas cookies and to think and prepare to come back to D.C. to work. (The Washington Post)

President Obama sharply curtailed his ambitions for legislation to avert the year-end “fiscal cliff” on Friday, urging Congress to adopt a stopgap measure to keep benefits flowing to unemployed workers and prevent taxes from rising on income under $250,000 a year.

The plan should also “lay the groundwork” for action next year to spur economic growth and rein in the national debt, Obama said at a White House news conference. But with taxes set to rise for virtually every American in just 10 days, Obama conceded that time was too short to enact far-reaching legislation now.

“I am still ready and willing to get a comprehensive package done. . . . I remain committed to working towards that goal, whether it happens all at once or whether it happens in several different steps,” Obama said.

“But in 10 days, we face a deadline,” he said. Protecting unemployed workers and 98 percent of taxpayers is “an achievable goal that can get done in 10 days.”

With that, Obama and his family boarded a flight to Hawaii for Christmas, leaving congressional leaders to untangle a long-standing political knot: how to push a tax hike of any kind through the fractious Republican House.

One day earlier, House Republicans rejected an alternative tax plan advanced by Speaker John A. Boehner (R-Ohio) that would have prevented taxes from rising on income under $1 million a year. It was torpedoed by conservatives who balked at the prospect of letting taxes go up for roughly 400,000 households.

Passing a bill with a $250,000 threshold would let taxes rise for about 3 million families, a much tougher political lift even in the Democratic-controlled Senate. On Friday, Senate Democrats said they were willing to take a more direct role in the talks, but that a compromise between Obama and Boehner remained critical to moving forward.

“We’re not going to want to come to a deal if we know Boehner isn’t going to move it in the House,” Sen. Charles E. Schumer (D-N.Y.) said. “The two key people are the president and the speaker, and until they come to an agreement, not much else is going to happen.”

While the shape of a deal depends on negotiations over the next few days, the more limited legislation Obama has proposed is likely to be narrowly focused on averting economic upheaval.

Democrats said they would seek to delay automatic spending cuts set to hit federal agency budgets next month. Both parties also want to prevent the alternative minimum tax from ensnaring millions of new taxpayers in April. And they want to preserve an array of expiring tax breaks that includes a popular credit for business research and development.

But a temporary payroll tax holiday will probably end in January, taking an immediate bite out of paychecks for most workers. And without a bipartisan agreement to significantly cut spending, Republicans will not grant Obama an increase in the limit on federal borrowing — which will probably be needed within the next two months if the government is to avoid defaulting on its obligations.

On Friday, Obama huddled at the White House with Senate Majority Leader Harry M. Reid (D-Nev.) before addressing reporters and spoke by telephone with Boehner. But the phone call appeared to do little to improve the prospects for a deal of any size.

“The House has already acted to stop all of the looming tax hikes and replace the automatic defense cuts” scheduled to hit in January, Boehner spokesman Brendan Buck said in a written statement, a reference to a measure the House passed last summer to extend the George W. Bush-era tax hikes for taxpayers at all income levels.

“It is time for the Democratic-run Senate to act,” Buck said, “and that is what the speaker told the president tonight.”

Senate Minority Leader Mitch McConnell (R-Ky.) was no more encouraging. In the past, McConnell has stepped in to resolve disputes between Boehner and the White House. But as he works to avoid a primary election challenge from the right in 2014, McConnell has deferred to Boehner on the fiscal cliff.

McConnell did so again Friday, calling on the Senate to take up the House-passed tax bill.

Some of his Republican colleagues, however, seemed almost eager to work something out. In recent weeks, at least 10 Senate Republicans have suggested that they would be willing let taxes rise on incomes over $250,000 a year in exchange for protecting middle-class families from any tax increase.

Sen. Lamar Alexander (R-Tenn.) complained Friday that Obama hadn’t reached out to a bipartisan group of senators who have for months been saying they would support a debt-reduction plan that raises taxes and curtails spending on federal health and retirement programs.

“He hasn’t talked to any of us. We might as well be watching a baseball game,” Alexander said.

“There are a lots of ways to put something together,” added retiring Sen. Jon Kyl (Ariz.), the No. 2 Senate Republican. Referring to Ronald Reagan’s joke about the little boy who was delighted to encounter a room full of horse manure, Kyl said, “It doesn’t look too good right now. But there’s got to be a pony in there somewhere.”

Like their counterparts in the House, Senate Republicans are eager to avert the fiscal cliff — Washington shorthand for more than $500 billion in automatic tax hikes and spending cuts set to hit in January. Unless Congress acts, taxes will rise for nearly 90 percent of Americans, potentially knocking the nation back into recession.

Polls showthat a majority of Americans would blame Republicans for that outcome. Surveys also show that voters overwhelmingly support Obama’s proposal to deal with record budget deficits in part by raising taxes on the wealthy.

For weeks, Obama and Boehner tried to forge consensus on a broad debt-reduction plan that would raise taxes on the rich while meeting GOP demands to restrain soaring spending on entitlement programs, like Social Security. As a compromise, Obama offered this week to revise his tax proposal so that only households making more than $400,000 a year would be affected.

But that effort stalled when Boehner decided to pursue a more partisan course that focused on raising taxes only for millionaires. Its embarrassing collapse left efforts to avoid the cliff in shambles.

At a Friday news conference, Boehner acknowledged that he cancelled a scheduled vote on his plan because his fellow Republicans would not support it.

“A perception [was] created that that vote last night was going to increase taxes,” Boehner said. “And we had a number of our members who just really didn’t want to be perceived as having raised taxes.”

Boehner said he continues to favor a grand bargain that would set the stage for a sweeping overhaul of the tax code and significant changes to federal health and retirement programs.